Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
6001	2^369643-1865767	111274	Enzo Doria	03/2016
6002	2^369603+885	111262	Lelio R Paula	05/2017
6003	25555^22564+22564^25555	111252	Hans Havermann	10/2020
6004	L(532277)	111240	Renaud Lifchitz	03/2004
6005	105^55033-2	111233	Lelio R Paula	10/2017
6006	(35*10^111232-737)/9	111233	Robert Price	07/2018
6007	26970^13307+13307^26970	111227	Hans Havermann	10/2020
6008	25419^23716+23716^25419	111210	Hans Havermann	10/2020
6009	9*10^111201-29	111202	Robert Price	09/2019
6010	2^369392+29835	111199	Lelio R Paula	05/2017
6011	3^233059+16	111198	Robert Price	03/2020
6012	2^369354-3413	111187	Yves Minet	12/2016
6013	2^369296-27	111170	Lelio R Paula	02/2013
6014	2^369239-109837	111153	Enzo Doria	05/2014
6015	2^369224-291839	111148	Enzo Doria	07/2015
6016	2^369216+2798881	111146	Enzo Doria	04/2016
6017	26842^13817+13817^26842	111137	Hans Havermann	11/2020
6018	(5*10^111119-191)/3	111120	Robert Price	05/2021
6019	(29*10^111112-23)/3	111113	Robert Price	03/2022
6020	10^111111+163849	111112	Patrick De Geest	03/2017
6021	10^111111-312911	111111	Patrick De Geest	03/2017
6022	2^369092-216923	111108	Enzo Doria	05/2014
6023	2^369081-55	111105	Lelio R Paula	02/2013
6024	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
6025	88^57124-87	111077	Norbert Schneider	11/2015
6026	2^368980+753	111075	Lelio R Paula	05/2013
6027	2^368946-3623	111064	Yves Minet	03/2017
6028	2^368929+29835	111059	Lelio R Paula	05/2017
6029	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
6030	111^54298+110	111057	Norbert Schneider	04/2017
6031	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
6032	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
6033	35799^1262+1262^35799	111015	Hans Havermann	10/2020
6034	(298*10^111004+11)/3	111006	Robert Price	11/2020
6035	27648^10349+10349^27648	111004	Hans Havermann	11/2020
6036	28899^6932+6932^28899	110997	Hans Havermann	11/2020
6037	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
6038	2^368641-460303	110972	Enzo Doria	06/2015
6039	2^368619-109087	110966	Enzo Doria	04/2014
6040	(74*10^110961+313)/9	110962	Robert Price	06/2019
6041	25258^24711+24711^25258	110956	Hans Havermann	11/2020
6042	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
6043	3*2^368489+7	110927	Lelio R Paula	09/2014
6044	(14*10^110922+61)/3	110923	Robert Price	12/2018
6045	97411!4-2	110913	Robert Price	07/2017
6046	(301*10^110903+23)/9	110905	Robert Price	06/2021
6047	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
6048	25830^19619+19619^25830	110880	Hans Havermann	10/2020
6049	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
6050	26022^18191+18191^26022	110850	Hans Havermann	10/2020
6051	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
6052	(37*10^110813+251)/9	110814	Robert Price	09/2021
6053	2^368050-64875	110795	Lelio R Paula	05/2017
6054	2^368048+25	110794	Lelio R Paula	02/2013
6055	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
6056	69^60239-2	110771	Lelio R Paula	10/2013
6057	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
6058	2^367924-69	110757	Lelio R Paula	02/2013
6059	(23*10^110738+61)/3	110739	Robert Price	01/2022
6060	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
6061	2^367709-109723	110692	Enzo Doria	04/2014
6062	2^367687+213413	110685	Enzo Doria	09/2023
6063	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
6064	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
6065	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
6066	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
6067	140^51515-139	110558	Norbert Schneider	04/2019
6068	2^367215+1879223	110543	Enzo Doria	09/2016
6069	25782^19375+19375^25782	110534	Hans Havermann	10/2020
6070	26117^17058+17058^26117	110526	Hans Havermann	10/2020
6071	2^367141+41	110521	Lelio R Paula	02/2013
6072	2^367126+29835	110516	Lelio R Paula	05/2017
6073	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
6074	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
6075	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
6076	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
6077	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
6078	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
6079	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
6080	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
6081	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
6082	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
6083	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
6084	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
6085	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
6086	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
6087	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
6088	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
6089	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
6090	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
6091	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
6092	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
6093	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
6094	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
6095	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
6096	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
6097	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
6098	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
6099	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
6100	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
6101	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
6102	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
6103	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
6104	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
6105	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
6106	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
6107	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
6108	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
6109	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
6110	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
6111	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
6112	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
6113	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
6114	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
6115	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
6116	(11*10^110496+49)/3	110497	Robert Price	07/2018
6117	25447^21958+21958^25447	110481	Hans Havermann	11/2020
6118	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
6119	7*10^110468-23	110469	Robert Price	07/2019
6120	5*3^231464-2^231464	110438	Jon Grantham	08/2023
6121	2^366853+5711	110434	Lelio R Paula	05/2017
6122	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
6123	2^366816+315	110423	Lelio R Paula	05/2017
6124	2^366775-2787037	110411	Enzo Doria	03/2016
6125	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
6126	2^366751+2797553	110404	Enzo Doria	03/2016
6127	25276^23331+23331^25276	110404	Hans Havermann	10/2020
6128	2^366748+255	110403	Lelio R Paula	05/2017
6129	2^366738-2985	110400	Yves Minet	09/2014
6130	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
6131	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
6132	2^366716+1871791	110393	Enzo Doria	05/2016
6133	(239*23^81066-349)/22	110391	Eric Chen	08/2023
6134	2^366649+1871687	110373	Enzo Doria	05/2016
6135	2^366629-351205	110367	Enzo Doria	06/2015
6136	(31*10^110363+257)/9	110364	Robert Price	12/2021
6137	(17*19^86292-215)/18	110347	Eric Chen	01/2023
6139	2^366558+1874479	110345	Enzo Doria	06/2016
6138	25132^24581+24581^25132	110345	Hans Havermann	10/2020
6140	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
6141	26368^15285+15285^26368	110331	Hans Havermann	10/2020
6142	(23*10^110290+19)/3	110291	Robert Price	07/2019
6143	18^87853-4409	110280	Enzo Doria	03/2013
6144	28490^7419+7419^28490	110267	Hans Havermann	11/2020
6145	2^366218-23	110243	Lelio R Paula	02/2013
6146	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
6147	2^366178-343991	110231	Enzo Doria	07/2015
6148	12^102123-11	110210	Riley Fisher	09/2023
6149	25777^18798+18798^25777	110174	Hans Havermann	10/2020
6150	2^365944+1871341	110161	Enzo Doria	05/2016
6151	2^365838-461267	110129	Enzo Doria	07/2015
6152	30152^4491+4491^30152	110126	Hans Havermann	11/2020
6153	2^365802+23359	110118	Enzo Doria	10/2023
6154	10^110111+464019	110112	Patrick De Geest	05/2021
6155	10^110111-40001	110111	Robert Price	01/2021
6156	2^365763-6555	110106	Lelio R Paula	04/2017
6157	(2^365689+2^182845+1)/5	110083		11/2006
6158	2^365666-459161	110077	Enzo Doria	05/2015
6159	3*10^110076-7	110077	Robert Price	08/2015
6160	13^98785-72	110041	Lelio R Paula	03/2017
6161	(25^78707+1)/26	110027	Robert Price	06/2013
6162	(7*10^110027-277)/9	110027	Robert Price	02/2022
6163	(16*10^110014-73)/3	110015	Robert Price	07/2020
6164	(7*10^110006-151)/9	110006	Robert Price	02/2018
6165	6^141361-7	110001	Lelio R Paula	11/2014
6166	20^84536+81	109984	Lelio R Paula	03/2017
6167	5*2^365347-9	109982	Lelio R Paula	09/2014
6168	9*6^141303+7	109957	Lelio R Paula	11/2014
6169	27635^9522+9522^27635	109953	Hans Havermann	11/2020
6170	78^58099+77	109929	Norbert Schneider	02/2015
6171	2*10^109928-7	109929	Robert Price	10/2015
6172	30580^3933+3933^30580	109927	Hans Havermann	11/2020
6173	26380^14689+14689^26380	109926	Hans Havermann	11/2020
6174	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
6175	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
6176	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
6177	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
6178	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
6179	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
6180	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
6181	(35*10^109888-89)/9	109889	Robert Price	02/2022
6182	18^87533-11	109878	Lelio R Paula	04/2017
6183	2^364982-5	109871	Henri Lifchitz	04/2006
6184	3*10^109861+59	109862	Robert Price	08/2018
6185	5*10^109860-69	109861	Robert Price	02/2021
6186	2^364936-1867979	109857	Enzo Doria	04/2016
6187	27013^11652+11652^27013	109846	Hans Havermann	10/2020
6188	2^364867-112087	109836	Enzo Doria	06/2014
6189	4^182415-85061	109825	Mike Oakes	06/2011
6190	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
6191	(53*10^109809-287)/9	109810	Robert Price	02/2022
6192	(52*10^109807-133)/9	109808	Robert Price	09/2021
6193	25708^18675+18675^25708	109806	Hans Havermann	10/2020
6194	(17^89227+16^89227)/33	109788	Robert Price	08/2013
6195	2^364687-187	109782	Lelio R Paula	01/2012
6196	2^364644+67	109769	Lelio R Paula	01/2012
6197	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
6198	(2^364616+5)/9	109760	Lelio R Paula	01/2014
6199	(55*10^109759+89)/9	109760	Robert Price	03/2019
6200	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
6201	12^101694+73	109747	Lelio R Paula	03/2017
6202	13^98518-66	109744	Lelio R Paula	03/2017
6203	(8*10^109721-269)/9	109721	Robert Price	09/2021
6204	2^364478-113261	109719	Enzo Doria	07/2014
6205	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
6206	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
6207	27814^8777+8777^27814	109681	Hans Havermann	10/2020
6208	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
6209	3^229824+340	109654	Lelio R Paula	03/2017
6210	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
6211	(2*10^109645-71)/3	109645	Robert Price	12/2017
6212	2^364169-112813	109626	Enzo Doria	06/2014
6213	28822^6359+6359^28822	109622	Hans Havermann	11/2020
6214	10^109615+21	109616	Lelio R Paula	03/2017
6215	10^109615-456267	109615	Patrick De Geest	03/2017
6216	2^364094-113	109604	Lelio R Paula	01/2012
6217	25251^21898+21898^25251	109600	Hans Havermann	11/2020
6218	(4^182026+11)/3	109591	Robert Price	02/2017
6219	2^364041-6883	109588	Lelio R Paula	09/2011
6220	12^101545+11	109586	Lelio R Paula	03/2017
6221	26536^13475+13475^26536	109582	Hans Havermann	11/2020
6222	2^363842-2787101	109528	Enzo Doria	03/2016
6223	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
6224	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
6225	2^363769+5711	109506	Lelio R Paula	04/2017
6226	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
6227	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
6228	p(22245)#/2-8	109462	Robert Price	01/2017
6229	2^363556+55	109442	Lelio R Paula	01/2012
6230	(509*10^109414+31)/9	109416	Robert Price	08/2022
6231	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
6232	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
6233	2^363406+1871569	109397	Enzo Doria	05/2016
6234	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
6235	(2^363349+7)/9	109378	Lelio R Paula	01/2014
6236	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
6237	3^229236+100	109374	Lelio R Paula	03/2017
6238	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
6239	2^363268-58695	109355	Lelio R Paula	04/2017
6240	2^363191-112321	109332	Enzo Doria	06/2014
6241	26231^14718+14718^26231	109327	Hans Havermann	10/2020
6242	25461^19672+19672^25461	109326	Hans Havermann	10/2020
6243	4*10^109316-63	109317	Robert Price	10/2018
6244	2^363120+3	109311	Donovan Johnson	04/2006
6245	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
6246	2^363042-114641	109287	Enzo Doria	04/2015
6247	2^363020-112793	109280	Enzo Doria	06/2014
6248	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
6249	(85*10^109253+203)/9	109254	Robert Price	09/2020
6250	24990^23431+23431^24990	109202	Hans Havermann	10/2020

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Probable Primes Top 10000

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